Sunday, January 26, 2014

Old Keynesian Economics and Equilibrium Theory

Noah Smith refers to a vintage piece by Robert Barro that pours scorn on the New Keynesian agenda. I am grateful to Noah for drawing our attention to it. I find much to agree with in Barro’s critique of the New Keynesians and those who would attack his position would be wise to heed the proverb: those who live in glass houses should not throw stones.

Much of the modern debate between classical and Keynesian economics is framed around equilibrium theory. In the red corner is a class of reactionary equilibrium theorists who are blind to the reality of mass unemployment. In the blue corner, is a class of enlightened new Keynesians who are champions of the unemployed. These progressives recognize that nominal rigidities prevent the labor market from equating demand and supply and the obvious remedy is large-scale fiscal expansion. The failure of the reactionaries to recognize the obvious merits of this argument must be due to their political motivation.

This is a simplistic description of reality, not just because both new-Keynesian and new classical economists span both sides of the political aisle. It is also simplistic because it misunderstands the modern meaning of the equilibrium assumption. Using general equilibrium theory, broadly defined, one can build sensible equilibrium models where high unemployment exists as one of many possible labor market equilibria.

Most of the macro-economists I know, and all of the macro-economists I respect, learned a huge amount from the rational expectations revolution, initiated by Robert Lucas. Drawing on Chapter 7 of Gerard Debreu’s Theory of Value, Lucas taught us to assume that markets are always in equilibrium. That observation was a game changer that is still playing out in the research community and its implications were not, in my view, fully understood by early adopters of classical economic models.

Most modern macroeconomic theorists use dynamic stochastic general equilibrium models, DSGE, for short. These models are direct descendants of John Hicks' classic book, Value and Capital, which developed the idea that economies evolve as a series of ‘weeks’, each of which is characterized by markets that are in what Hicks called a ‘temporary equilibrium’.

After reading Keynes’ General Theory, Hicks renounced the equilibrium assumption (see Michel De Vroey) and argued instead, that for some commodities, demand may not equal supply in any given week. That ‘disequilibrium’ assumption, came to dominate the subsequent development of macroeconomics and it manifests itself today in new-Keynesian models of sticky prices.

The disequilibrium assumption favored by Hicks came under attack in the 1970s because simple models of that era could not account for the simultaneous occurrence of inflation and unemployment.

The main tool used to understand macroeconomics in 1970 was the IS-LM model. That model was widely perceived to be unsatisfactory, in part, because it is purely static. The IS-LM model does not explain the interaction of prices and expectations and, for that reason, it is an unsatisfactory model if one is interested in understanding inflation, which is an inherently dynamic process. That problem was solved by the introduction of mathematical techniques that were unavailable to previous generations of theorists. Those techniques were introduced to macroeconomics in the rational expectations revolution.

The rational expectations revolution made two changes to the temporary equilibrium agenda as it was understood in 1972. First, rational expectations theorists insisted that markets are in equilibrium every period. According to this approach, the demand equals the supply for every commodity; including labor. Second, rational expectations theorists insisted that expectations of future prices are correct in the sense that no agent is systematically fooled into making decisions that he subsequently regrets. Early versions of rational expectations models also assumed a single agent, perfect competition, linear technologies, etc., etc., etc.

These early equilibrium models, (the RBC model of Kydland and Prescott is a good example), carried with them a very strong implication. There is nothing that government can do to improve the welfare of the agents in the model. In the language of economics; these models have a unique equilibrium and that equilibrium is Pareto Optimal.1

Many economists have recognized for a long time that the RBC model of Kydland and Prescott is not a good description of the real world. Larry Summers, for example, tells us that the classical vision of economics is nonsense because it disregards some basic facts; primary among them is the existence of large-scale unemployment that persists for decades. I agree whole-heartedly. But accepting equilibrium theory as an organizing principle does not require that we accept all of the assumptions of the RBC model.

The problem with classical models is not the equilibrium assumption; it is the optimality implication. The idea that the current state of affairs is socially optimal is so obviously at odds with the existence of mass unemployment that it has given equilibrium theory a bad name. In very simple models, equilibrium and optimality are the same thing. But that conclusion is a very special implication of some equilibrium models. It does not hold in general. That idea is key to reconciling Keynesian economics with equilibrium theory.

The sceptical reader will reasonably ask how equilibrium can be consistent with unemployment. Surely the existence of unemployment requires us to assume that the demand and supply of labor are not equal to each other. Not so: By modelling the process by which unemployed workers are matched with jobs, we can use search theory (for which Dale Mortensen, Chris Pissarides and Peter Diamond were awarded the 2010 Nobel prize) to understand how unemployment varies over time.

To understand the persistence of high unemployment, we do not need to assume that prices are sticky or that markets are in disequilibrium. Mass unemployment does not occur because markets are in disequilibrium: Mass unemployment occurs because the market equilibrium is not socially optimal. Recognizing that simple fact has important implications for our understanding of the current state of the world economy.

This post would not be complete without commenting on a claim that Paul Krugman recently made on his blog in the New York Times. In Krugman’s view we should return to what he refers to as Neo-Paleo-Keynesianism which, according to Krugman, involves
…turning away from hard math back toward rough-and-ready assumptions based on empirical observation. Aspiring up-and-coming economists may be able to publish empirical papers in this vein, but theoretical analyses are likely to be met with giggles and whispers. Just because the stuff works doesn’t mean that it will be publishable.
I disagree and in a recent blog post I suggested a different definition of Neo-Paleo-Keynesianism from Krugman's initial use of that term.  In 2008 I defined a way of reconciling Keynesian economics with equilibrium theory that I called Old-Keynesian Economics. Both of these links describe ways of reconciling the essence of Old Keynesian economics with equilibrium theory that go well beyond “rough-and-ready assumptions based on empirical observation”.

The challenge for aspiring up-and-coming economists is to reconcile the observation of persistent mass unemployment with the tools of economics by building on the foundation provided by the recent work of DSGE theorists. Often, that will involve mastering ‘hard math’ because hard math offers the best way of consistently formalizing the logic that underlies economic theory. The combination of search theory with temporary equilibrium theory offers the tools to do just that. No-one would use an abacus when offered a computer. For the same reason, it would be unwise for an aspiring up-and-coming economist to cling to the static IS-LM model when there are alternative tools available that are better suited to the task of explaining financial crises.
1. To the unsuspecting natural scientist reading this blog -- economists use the word equilibrium to mean that plans of agents are internally consistent. There is no implication in an ‘equilibrium’ that observable variables are constant through time. Instead, they are typically described by a stationary probability measure.


  1. There is something to be said for defining "equilibrium" as: "that which the model predicts".

    I think I prefer your definition of Neo-paleo-Keynesian, because the neo is not redundant.

    1. Nick. There are two uses of equilibrium here. One is that markets are in equilibrium in each 'week'. The other is that expectations are not consistently wrong. Your definition applies, I think, to the second.

  2. Hi Roger, can you clarify one point? In the endnote, you write, "economists use the word equilibrium to mean that plans of agents are internally consistent." Do you mean that each agent's plan is internally consistent or that all agents' plans are mutually consistent?

    1. Greg. You are of course correct, "mutually consistent" would be better language.

  3. Including expectations, good. Including rational expectations, not yet complete.
    I think you are saying expectations need to be in the model. YES
    I think you then say the IS-LM doesn't include expectations. Tricky, Keynes was an expectations man, so... anyone interested in IS-LM building from Keynes analysis won't really find that a useful criticism.
    And then you imply that Rational Expectations are an improvement. Well, how does this not just confuse the issue? The questions about RE aren't about the E, they are about the R.
    RE is clearly an incomplete description of where E's come from.
    Will hard math help arrive at a deeper understanding of E's? Only loosely, hard math is best suited for helping work with a given understanding and for helping to understand the implications and interactions of the assumptions that flow from a given understanding. The process goes both ways, from math to understanding and from understanding to math, however, it seems clear to anyone who isn't a hard math guy that beginning with math is very problematic because it regularly leads to simply more math and less understanding. Indeed RE is just such an example. better and harder math won't ever improve the flaws in the R assumption. I say young bright economists should spend more time on understanding and less time on math - if they have to choose. The really bright ones should just do both, and with any luck the R will get improved upon.

    1. Dan. My criticism of IS-LM is that it is static, not so much that expectations don't enter. As for the interaction of understanding math and data: yes you are right. As for the assumption of rational expectations: that is a philosophical minefield. In my view, we can make a lot of progress with models where there is a continuum of RE equilibria and, in those models, it is very difficult to disentangle RE equilibria from non RE equilibria.

  4. I'm generally sympathetic to your research agenda and you are probably right about some of these issues, but I think overall your views on this are dangerous--even for your own research project.

    The big thing that bugs me are your views about equilibrium. So, as it happens I've done work in game theory and I have a lot of experience in physics--in particular equilibrium statistical mechanics. From neither perspective do your views hold up.

    In terms of pure game theory, I don't think you fully appreciate that "equilibrium" can mean practically anything (I'll say more about this in a moment). For now, the only point I want to make is that the statement "system X is in equilibrium" is a nearly meaningless theoretical statement in and of itself.

    I think the view from physics is even more helpful, though. Here there is also a sense in which most things can be described by equlibrium. Any system which satisfies the adiabatic theorem can understood in this way. Of course, this leaves out turbulence which fails the adiabatic theorem... and that means that you can't understand things like thunderstorms as equilibrium phenomenon. Is a thunderstorm like a financial crisis? Maybe. But it gets worse than that. Even with systems that could in theory be understood as equilibrium phenomenon, equilibrium is not necessarily the best way to understand them. Take wind. You could understand a steady wind as an equilibrium phenomenon, but no one does that. Instead, you'd split the system in two (high and low pressure) and model air movement between them as a disequilibrium dynamic process... wind. This has a name: the adiabatic approximation. "Equilibrium" inside the two systems are "fast" so that pressure is constant (or close enough not to matter) and the wind, altering that initial pressure pattern, is "slow". For this reason, I like to refer to this sort of model as "equilibrium-disequilibrium".

    The thing is, using this kind of equilibrium-disequilibrium approach requires you to know much less about the underlying system while still getting basically the right answer. It also helps us to understand better what's really going on (believe me, understanding wind purely as a statistical bias in molecular collisions would not be very insightful). To finish up, the last thing I'd point out is that AS-AD and IS-LM really are just (simple) applications of the same equilibrium-disequilibrium approach.

    Wedding yourself to an equilibrium approach does not, or at least should not, in itself be a sign that you're doing anything worthwhile.

    1. Just let me add one more point.

      Your specific argument that you could handle unemployment with search models really underlines my point. In a sense, you COULD do something like that, but you're risking getting the wrong answer. Why? Because the problem in recessions is that there aren't enough jobs opening up--you can see that in the JOLTS data clear as day--and search theory won't help with THAT. By putting all your theoretical eggs in the one basket of equilibrium... well, I was about to say you're just going to make models that are too hard to solve, but really we're well past that point now, aren't we?

    2. bseconomist:

      "I don't think you fully appreciate that "equilibrium" can mean practically anything"

      I agree with that statement. Equilibrium is, for me, an organizing principle.

      Trying to transfer analogies from physics is treacherous and misleading. The word "equilibrium" does not mean the same thing in economics as it does in physics. But you clearly understand that since you are familiar with game theory.

      "Wedding yourself to an equilibrium approach does not, or at least should not, in itself be a sign that you're doing anything worthwhile."

      Agreed. The sign that the approach is progressive will be its ability to explain new data sets and or new facts.

  5. Roger, my understanding is that Hicks advocated use of the temporary equilibrium concept precisely to describe a situation in which all existing markets clear but the intertemporal plans of individuals are not necessarily mutually consistent. As time elapses, some expectations are disappointed, and beliefs are revised. The economy therefore follows a sequence of temporary equilibria with changing beliefs. One equilibrium condition (market clearing) is continuously satisfied while another (mutually consistent beliefs) is not.

    It seems to me that this conception of economic dynamics is quite different from one in which there are multiple RE paths and hence some indeterminacy in which one is selected. For instance, mutually inconsistent beliefs allow for active trading and speculation, even involving large zero sum bets of the kind we see routinely in financial markets.

    1. Rajiv: You are correct; that is also my understanding of Hicks. However, I see the consistency of expectations with outcomes as a necessary property of a system in which the fundamentals are governed by a stationary process.

      Jean-Michel Grandmont has interesting work in which the learning rule NEVER converges to a rational expectations equilibrium. That's an interesting idea, but I'm not sure it leads to a positive theory that can help explain the interaction of policy with observed outcomes.

      In my work, there is a separate object called a "belief function" that is a positive model of "animal spirits". Because my models have incomplete factor markets, the belief function coexists with the rational expectations assumption. It's not necessary to also impose the rational expectations assumption, but a lot can happen even when I do impose it. I'm content, for the time being, to assume rational expectations and see where it leads.

    2. Roger, in reply to Rajiv's comment, you write, “I see the consistency of expectations with outcomes as a necessary property of a system in which the fundamentals are governed by a stationary process.”

      What a marvelously lucid statement of RE’s rarely articulated basic premise! I think it was just this premise that John Hicks eventually rejected. I can’t remember all the details, but I believe Hicks said that Paul Davidson eventually convinced him that economic processes aren’t ergodic, hence there’s no timeless probability distribution around which expectations can converge. So Hicks started looking for a model in which the agents “do not know what is going to happen and know that they do not what is going to happen. As in history!” (Hicks, "Causality in Economics," 1979).

  6. Greg. You are right of course.

    The learning literature has much to recommend it. But whatever learning rule one uses to replace RE; I believe that it should have the property that the rule converges to RE if the fundamentals remain stationary for long enough.

    One reason for maintaining RE is that it provides us with a parsimonious explanation for 'announcement effects'. When Ben Bernanke or Mark Carney make statements about likely future bank actions: markets move immediately. RE models capture that idea by solving out for 'forward roots'. So called 'jump variables' are not simply a mathematical convenience; their effects are observed in practice, at least in the financial markets.

    The question then arises; why don't we the effects of jump variables in goods markets and labor markets? Hicks' answer was that some markets are 'flex price' and some are 'fix price'. My answer, is that factor markets are incomplete and that wages and prices do not have to adjust to maintain an equilibrium in the labor market.

    1. Thank you, Roger. These are very intriguing ideas, worth puzzling over!

  7. Thanks to Roger for taking the time to write this post. Coming from someone who has engaged in such a serious manner with the ideas of Keynes, I think this will have more resonance to the audience most suspicious of equilibrium analysis than the same message would coming from most others.

    Lucas, in Models of Business Cycles, wrote beautifully many years ago about how little progress is made by “hamstringing the auctioneer” in a model where the commodity space is abstract units of labor time. This is why, if ones care about unemployment, one will model search—not foolishly insist on trade of labor services at linear non-market-clearing prices. After all, a model of price-takers who can’t count on being able to sell labor is a pretty incoherent model. This is why market clearing goes with price-taking; You can’t have the latter without the former. If you don’t like market clearing, don’t model agents as price taking—model the actual problem you think they face: not being able to find a “job” (as opposed to not being able to find buyers for a quantity of labor time they want to sell on a given day). And this will immediately get you to Roger’s point: equilibrium in this setting may be terrible for agents as a matter of their well-being.

    Additionally, allowing the modeling economist to assign non-mutually-consistent expectations to account for phenomena should strike just this constituency as a very dangerous thing—you really want to empower economists in this way? A famous person has said: “beware of economists bearing free parameters.” I think he meant to warn the public at large.

    1. Kartik,

      I believe you’re right in thinking that Roger’s work will be more resonant with “Keynesians” than the work of those who simply reject The General Theory out of hand.

      You go on to say that “allowing the modeling economist to assign non-mutually-consistent expectations to account for phenomena should strike just this constituency [Keynesian sympathizers] as a very dangerous thing—you really want to empower economists in this way?”

      I can’t make sense of this. I think you’d agree that, as matter of fact, market participants don’t have mutually consistent expectations (e.g., the “bulls” and the “bears”). Granted, some, like Milton Friedman, insist that the realism of a theory’s assumptions don’t matter. But this view, and positivism more generally, is a now a minority view among philosophers of science (see, e.g., Hilary Putnam’s work).

      And the critics of RE aren’t just the Keynesians and Post-Keynesians. In a 1995 interview with the Minneapolis Fed, Kenneth Arrow was asked what he thought of RE, and he replied, “there aren't enough repetitions to justify rational expectations. The world is changing. We're not really proceeding on a stationary basis.” And ten years later, in a 2005 interview with Juan Dubra, Arrow repeated his criticism and went on to ridicule Harold Cole and Lee Ohanian’s JPE paper, “New Deal Policies and the Persistence of the Great Depression: A General Equilibrium Analysis.”

      I can only speak for myself, but I’m not worried about “empowering economists” to build disequilibrium macro models. In fact, I wish they’d do more of it.

    2. Greg and Kartik. I've not read Hilary Putnam: do you have a recommended place to start? Whatever the consensus view among philosophers of science, I remain in the 'realistic assumptions don't matter' camp. I'm not even sure what it means for assumptions to be realistic.

      As for RE. I'm with Kartik. We can go a long way with the rational expectations assumption. There are aspects of the world that RE will miss: but an economic model cannot explain everything. That's also true in the natural sciences. Physics, for example, has one theory that works well at small scale, quantum theory, and another that works at large scale, general relativity.

      And to come back to realism: after reading Richard Feinman on quantum theory I realize that the assumptions of economic models can get a great deal more bizarre before they come close to the strangeness of the assumptions that underpin successful theories in the natural sciences.

  8. HI Greg--I had a written a reply from an iPad, which then got deleted when I tried to post. So here's the cliff notes version: I'm like many in hoping that definitive (not necessarily more realistic) models of expectations formation will show up--in many of the most pressing cases (a sudden crisis, etc) this seems vital. But right now, I don't know that there's a single compelling alternative that we should use instead of RE, so until then, I personally will stick to the industry standard, warts and all. Instead, I'll focus my attention on various other sorts of problems in trading arrangements (limted commitment, adverse selection) in making equilibrium outcomes less than ideal.

    As for Arrow--for me personally, he's the greatest economist of the past 100+ years, and he's probably right that often, the world denies us the stationarity to make RE super compelling. I guess I still like Hal and Lee's paper a lot. They wrote something down, parameterized it, and reported back. We should be grateful--It is the clarity of their approach that enables one to complain, as some are, about what they *did*, and not about what they might have *meant*.

    Best Regards


    1. Roger,

      I’d recommend Putnam’s “Philosophy in an Age of Science: Physics, Mathematics, and Skepticism” especially in light your interest in physics and the peculiarities of quantum theory. Putnam made major contributions to mathematics before turning to philosophy. He even tried to work out a new logic for the quantum theory. He’s thoughtful (has changed his mind many times) and is a pleasure to read.

      On the issue of assumptions versus predictions, here’s a little piece by Daniel Hausman, “Why Look Under the Hood,” (, which is brief, fun to read, and pertinent to Friedman’s methodological claims.

      Given the vast differences between the picture of the economy that emerges from your models, and the picture of the economy that emerges from, say, the Real Business Cycle School, I wonder whether the RE assumption and its application is really uniform across all its practitioners. In any event, I’m mainly interested in methodological pluralism.


      Your point about the paper Arrow criticizes is well taken: clarity is a very good thing. Your book awaits me when I return home this weekend, and I look forward to reading it.

      Best regards to you and Roger, Greg

    2. Greg-

      The clarity issue is paramount for me, and most of the rest of the guys I know. But it definitely requires being at peace with playing only a small part in a much longer and bigger cumulative process--and one that, yes, may be overthrown down the road anyway.

      re: my book--thanks for grabbing a copy--I'll refund the two bucks or so I get if you hate it :)....but I really think it's pretty reasonable.

      Best Regards


  9. Roger Farmer,
    A very clear articulation of some of the arguments for the current approach to macro. Let me say why they seem unconvincing to outsiders.

    Stationarity: We do not live in a stationary stochastic environment, so what's the point?

    Of course, there are many contexts in which the assumption of stationarity may be benign or even useful. Such use is not the what the criticism is about. The criticism is about the insistence on RE/stationarity.

    Equilibrium as an organizing principle: This risks turning you approach into a Popperian caricature -- one that can 'explain' everything but predict nothing. All you end up with is an arbitrary taxonomy.

    Suppose a certain aspect of time-series behaviour is due to heterogeneous beliefs and mutual inconsistency of plans. You can very well interpret it in terms of RE. The problem is that your estimated model will fit or 'explain' the data till time t (ie now), but then fail at time t + n. The model can be modified to fit again but it will fail again at t+2n, and so on ad infinitum If you start from an arbitrary (wrong) model, non-convergence to the 'correct' model is virtually guaranteed.

    Parsimony: Parsimony is certainly a desirable property. Unfortunately, it seems to me that macroeconomists misunderstand the point of Okham's razor. Arbitrarily restricting parameters, on apriori grounds, without first demonstrating correctness is not parsimony. Suppose we have multiple models that perform very well out-of-sample, then choosing one with the fewest parameters is perfectly justified. Incidentally, if we add arbitrary free parameters to make the model fit the data in-sample, it will perform poorly out-of-sample, which is why it will be rejected.

    Even if you ignore the previous point, the fact remains that, in practice, RE models (DSGEs) are not in fact parsimonious.

    Peter Howitt:
    "... empirical implementations of the new models that are actually used in central banks have had to reinsert the lagged variables in order to fit the data. Of course we can now tell stories that would make the coefficients of the lagged variables structural, ... So ... the issue is not that anything has been replaced but that rational expectations have been added as additional variables. While the assumption of rational expectations by itself has the virtues of parsimony and elegance, the process of adding rational expectations to the list of variables that were already considered as proxying for expectations has neither of these virtues."

    Realism of assumptions: I was initially stunned to read your claim that quantum mechanics makes unrealistic assumptions, until I realized that you were using a somewhat unusual definition of 'realism'.

    You use 'realism' to mean consistent with commonsense notions of behaviour, and reject the usefulness of realism in this sense. This is a perfectly justifiable position. However, others use 'realism' to mean consistent with evidence or empirically validated. The assumptions of QM pass the latter test, the assumptions of economic models usually do not. This makes all the difference in the world.

  10. Hermanq
    Thank you for your comments. I have addressed the critique of RE on a new post and In agree of much of what you say about most DSGE models. But much of the criticism you level does not, in my view, apply the the multiple equilibrium DSGE models that I work with.

    As for the equilibrium assumption as an organizing principle.

    Tautological assumptions are not unique to economics; they characterize ALL of science. They are what Imré Lakatos has called the hard core of a scientific research program.

    A parallel assumption in Physics, to the equilibrium assumption in economics, is Newton’s concept of 'action at a distance'. Action at a distance was a clear advance over Aristotle's notion of ‘action through contact’ that preceded it. But the notion of action at a distance does not presuppose Newton's laws. There are many other ways of describing physical phenomena that are consistent with that principle but which are distinct from from Newtonian mechanics.

    The same is true of the equilibrium concept in economics. That concept is given content by making specific assumptions about the connections between the economic concepts that we measure; inflation, unemployment and interest rates. For example, real business cycle economists assume that observable variables behave as if they were chosen by a single representative agent maximizing the expected value of an inter temporal utility function. In my work I adopt the equilibrium assumption but I make very different assumptions about the environment.

    We can accept the equilibrium assumption without accepting that either real business cycle models or new-Keynesian models are good descriptions of the world.

  11. Roger Farmer,
    I read your latest post on RE but will comment here for continuity.

    While I disagree with you on methodology, I find many of the ideas in your work both interesting and important. Which is why I read your blog.

    You are, of course, correct that tautologies can be found in Physics too. However, i) entire theories or models aren't treated as tautologies, and ii) Models incorporating those tautologies have incredible out-of-sample performance. There are no arbitrary tautologies that exist without out-of-sample empirical validation of the theories/models in which they are used.


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